Problem: Simplify the following expression: $\dfrac{48a^4}{96a^2}$ You can assume $a \neq 0$.
Solution: $ \dfrac{48a^4}{96a^2} = \dfrac{48}{96} \cdot \dfrac{a^4}{a^2} $ To simplify $\frac{48}{96}$ , find the greatest common factor (GCD) of $48$ and $96$ $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(48, 96) = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 48 $ $ \dfrac{48}{96} \cdot \dfrac{a^4}{a^2} = \dfrac{48 \cdot 1}{48 \cdot 2} \cdot \dfrac{a^4}{a^2} $ $\phantom{ \dfrac{48}{96} \cdot \dfrac{4}{2}} = \dfrac{1}{2} \cdot \dfrac{a^4}{a^2} $ $ \dfrac{a^4}{a^2} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a} = a^2 $ $ \dfrac{1}{2} \cdot a^2 = \dfrac{a^2}{2} $